This paper proposes an improved variant of the arithmetic optimization algorithm (AOA), called LMRAOA, which is used to solve numerical and engineering problems. Various strategies are proposed to improve AOA. First, Multi-Leader Wandering Around Search Strategy (MLWAS) is proposed to improve the exploration ability of the algorithm on global scale. Then, Random High-Speed Jumping Strategy (RHSJ) is proposed, and the search agent performs high-speed search in the current neighborhood to improve the exploitation ability. Finally, in order to avoid local optima, adaptive lens opposition-based learning strategy is proposed, and linear changes are proposed in its parameters to further satisfy the dynamic changes. 27 classic benchmark functions, 6 engineering optimization problems, and CEC2014, CEC2019 and CEC2020 competition functions are tested by LMRAOA algorithm and comparison algorithm. The experimental results show that, in most cases, the LMRAOA outperforms other algorithms in solving engineering and numerical problems, and can provide effective solutions.